Astron. Astrophys. 334, 99–109 (1998) ASTRONOMY AND ASTROPHYSICS Evolution of the colour-magnitude relation of early-type in distant clusters

Tadayuki Kodama1,2, Nobuo Arimoto2,4, Amy J. Barger1,3, and Alfonso Aragon-Salamanca´ 1 1 Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK ([email protected]) 2 Institute of Astronomy, University of Tokyo, Mitaka, Tokyo 181, Japan 3 Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, Hawaii 96822, USA 4 Observatoire de Paris, Section de Meudon, DAEC, F-92195 Meudon Principle Cedex, France

Received 21 November 1997 / Accepted 17 February 1998

Abstract. We present a thorough quantitative analysis of the models of elliptical galaxies with the C-M diagrams for early- evolution of the colour-magnitude relation for early-type galax- type galaxies in two distant clusters, Abell 2390 at z =0.228 ies in 17 distant clusters with 0.31

Table 1. Cluster samples and the regression lines for the C-M relations.

cluster z N1 N2 d.a. colour mag M0 ABref AC 103 0.31 25 4 28 R702 − KKrest −25 3.23 ± 0.04 −0.047 ± 0.065 1 25 4 28 I − KKrest −25 2.70 ± 0.04 −0.054 ± 0.052 1 AC 114 0.31 30 4 28 R702 − KKrest −25 3.13 ± 0.03 −0.027 ± 0.032 1 30 4 28 I − KKrest −25 3.33 ± 0.02 −0.083 ± 0.024 1 AC 118 0.31 35 3 28 R702 − KKrest −25 3.04 ± 0.03 −0.115 ± 0.027 1 35 4 28 I − KKrest −25 2.77 ± 0.02 −0.134 ± 0.028 1 Cl 0024 + 16 0.39 28 0 32 I814 − KKrest −25 3.08 ± 0.02 −0.091 ± 0.028 1 3C 295 0.461 25 — 24 V − KKT −25.5 4.98 ± 0.07 −0.09 ± 0.04 3 T Cl 0412 − 65 0.510 29 9 10 V555 − I814 I814 −22 2.32 ± 0.03 −0.091 ± 0.029 2 29 — 24 V − KKT −25.5 5.30 ± 0.06 −0.09 ± 0.04 3 GHO 1601 + 4253 0.539 42 — 26 V − KKT −25.5 5.33 ± 0.06 −0.09 ± 0.04 3 MS 0451.6 − 0306 0.539 51 — 26 V − KKT −25.5 5.24 ± 0.06 −0.12 ± 0.03 3 Cl 0016 + 16 0.546 25 4 36 I814 − KKrest −25 2.87 ± 0.02 −0.046 ± 0.031 1 T 106 15 10 V555 − I814 I814 −22 2.38 ± 0.01 −0.067 ± 0.010 2 65 — 26 V − KKT −25.5 5.20 ± 0.07 −0.08 ± 0.02 3 T Cl 0054 − 27 0.563 36 6 10 V555 − I814 I814 −22 2.28 ± 0.02 −0.090 ± 0.015 2 38 — 26 V − KKT −25.5 5.34 ± 0.06 −0.14 ± 0.03 3 3C 220.1 0.620 22 — 27 V − KKT −25.5 5.62 ± 0.07 −0.13 ± 0.04 3 3C 34 0.689 19 — 24 V − KKT −25.5 5.78 ± 0.06 −0.11 ± 0.04 3 GHO 1322 + 3027 0.751 23 — 24 R − KKT −26 4.56 ± 0.06 −0.07 ± 0.03 3 MS 1054.5 − 032 0.828 71 — 22 R − KKT −26 4.85 ± 0.06 −0.11 ± 0.02 3 GHO 1603 + 4313 0.895 23 — 21 R − KKT −26 5.01 ± 0.06 −0.13 ± 0.03 3 3C 324 1.206 13 1 — R − KK−26 5.84 ± 0.05 −0.099 ± 0.065 4 CIG J0848 + 4453 1.273 6 0 17 R − KK †5.92 ± 0.25 5 N1 — total number of ellipticals, N2 — number of excluded objects, d.a. — diameter aperture in kpc, † M0 — absolute magnitude of C-M zero-point, A and B — coefficients of C-M relation ( shows average colour). , refs. — 1: Barger et al. (1997), 2: Ellis et al. (1997), 3: Stanford et al. (1998), 4: Dickinson (1996), 5: Stanford et al. (1997) analysis because of their anomalous colours (see discussion be- early-type classes became increasingly uncertain. Principally low). Column 5 gives the adopted apertures in which the colour for this reason we have decided not to attempt to separately an- and magnitude measurements were made, in units of kpc. Note alyze the elliptical and S0 galaxy populations. This will also that the I814 magnitudes from E97 and the K magnitudes from increase our sample size and hence improve the statistics. Since SED98 are total magnitudes, as indicated by the subscript T . E97 found no evidence for a distinction between the C-M re- The colours and magnitudes used to define the C-M relation for lations for the E and S0 populations, our decision to combine each cluster are given in Columns 6 and 7, respectively. The sub- these morphological types should not affect the results of our script ‘rest’ means the magnitude is in the rest frame; all others analysis. Moreover, Dressler et al. (1997) point out that the num- are given in the frame of the observer. Column 8 lists the ab- ber fraction of S0 galaxies in clusters are rapidly decreasing as solute magnitude, M0, which defines the zero-point of the C-M a function of redshift, and above redshift 0.6 or so, S0 galaxies relation for each cluster, and Columns 9 and 10 give the cor- could almost disappear. responding C-M relation regression coefficients (see Sect. 2.2). To construct our C-M diagrams, we use ground-based I and Finally, Column 11 lists the references for the data. K-band data for AC 103, AC 114 and AC 118 from Barger et al. (1996) and ground-based K-band data for Cl 0024+16 2.2. Colour-magnitude relations and Cl 0016+16 from Barger et al. (1997). We also use ex- isting HST optical data in either the R702 or I814 bands. We For five clusters, AC 103, AC 114, AC 118, Cl 0024+16, and selected magnitude limits such that the samples would con- Cl 0016+16, we have used the morphological classifications tain approximately the brightest 3 mag in the K band. The ac- given in Couch et al. (1997) and Smail et al. (1997) to select a tual absolute magnitude limits depend on the depth of the K- sample of isolated (i.e. uncontaminated by nearby objects which band images and the redshift of the clusters, but they all lie would distort the colours) early-type (E, E/S0, or S0) galaxies between MK = −23 and −24. We present K-band magnitudes from the cluster cores. as absolute magnitudes in the rest frame for the clusters in our The reliability of the morphological selection of spheroidal sub-sample. The k-corrections are determined from a typical galaxies in clusters at z ∼ 0.55 was examined in detail by E97. spectral energy distribution (SED) of giant elliptical galaxies Visual classifications were found to be robust to I814 ≤ 21.0,but (Aragon-Salamamca´ et al. 1993). The SED changes along the over the interval I814 =21.0 −22.0 the distinction between the C-M relation and hence the correct amount of k-correction is 102 T. Kodama et al.: Evolution of the colour-magnitude relation of early-type galaxies in distant clusters

T varied towards fainter galaxies, however this effect is negligible. spheroidal galaxies with apparent I814 magnitudes brighter than Acording to the model SEDs, the difference in the k-correction 23 mag, are taken from their paper with the zero-points colours T across the C-M relation is about only 0.1 magnitude at most, transformed to those at the absolute magnitude I814 = −23. and the effect on both the C-M slopes and the zero-points are The slopes and zero-points of the C-M relations for the SED98 negligible in our analysis. The seeing corrections are made from sample have been taken from their paper as well. We adopted an estimate of how much light falls outside the adopted aper- their V − K colours for 8 clusters between z =0.461 and ture due to scattering, and the Galactic extinction corrections 0.689, and R−K colours for 3 clusters beyond that redshift, all are determined from the E(B − V ) values toward the clusters of which are referred as blue − K colours in their paper. Since as estimated by the HI intensity (Burstein & Heiles 1984). We they do not give the absolute colours of the C-M relation, we adopt E(B − V )=0.04 for AC 114, 0.05 for AC 103, 0.055 estimate the zero-points at M0 from the absolute colours of their for AC 118, and 0.03 for Cl 0024+16 and Cl 0016+16. no-evolution C-M relation at M0 and the average colour differ- For the high redshift cluster 3C 324 at z =1.206,we ence from it, both of which are given in the figures in SED98. adopted R − K colours and K magnitudes of 13 galaxies in the We note that the errors in zero-point ‘A’ in Table 1 include ‘red finger’ with K<19 mag (Dickinson 1996). These galax- only the random errors of the data; the systematic errors of the ies have been confirmed to be early-types from HST WFPC2 photometry are not included, except for the SED98 sample. We imaging. discuss the systematic errors further in Sect. 4.2. Fig. 1 shows the C-M diagrams for the early-type galaxies in For the most distant cluster CIG J0848 + 4453 at z =1.273, our sub-sample of six clusters above. The open circles with filled we adopt R − K colours and K magnitudes of the six dots represent the spectroscopically confirmed members. The spectroscopically-confirmed cluster members for supplemen- crosses indicate the objects whose colours place them clearly tal use, although morphology is unknown (Stanford et al. 1997). outside the C-M relation. Although there are very few such The C-M relation, however, cannot be defined due to the paucity objects in our sample (see N2 in Table 1), we have excluded them of the number of galaxies. Thus, we measure the average colour from our analysis since their anomalous colours could distort and the standard deviation of the colours using the error of each the global statistics. Most of these excluded objects are likely colour as a weight, and regard these results as the zero-point to be non-members, but it is possible that a fraction of the bluer colour and its error. These numbers are also listed in Table 1. objects are members that have recently undergone strong star formation. However, these excluded objects only account for a very small fraction (i.e. 5 %) of the total stellar mass in the early- 3. Model type galaxies in our six sub-sample clusters (estimated from the 3.1. Evolution of the colour-magnitude relation K-band luminosity), hence they will not affect our analysis of the bulk of the stellar population. The remainder of the galaxies The elliptical galaxy models we have used are essentially the are represented with filled circles. Photometric random errors same as those built by KA97 (see also Kodama 1997 for details). are shown only for 3C 324. All the other clusters have negligibly Following Larson (1974) and Arimoto & Yoshii (1987), we as- small errors, smaller than the size of the symbols. sume elliptical galaxy formation occurs in a monolithic collapse We calculate the C-M regression lines using the BCES (bi- accompanied by a galactic wind. Star formation is burst-like variate, correlate errors and scatter) method of Akritas & Ber- with very short star-formation and gas-infall time-scales (both shady (1996), who have kindly provided us with their software. are set to be 0.1 Gyr) followed by a galactic wind which occurs Their program gives both the regression lines and the fitting er- less than 0.5 Gyr from the start of galaxy formation. Chemical rors analytically, considering the errors in both the magnitudes evolution is taken into account consistently under a well-mixed and the colours, as well as the intrinsic scatter of the data. The approximation. The model is calibrated to the C-M relation of covariant errors are assumed to be equal to the errors in the Coma in the V − K v.s. MV plane (BLE92) at z =0, either by magnitudes since the magnitude errors dominate the errors in changing the mean stellar metallicity (metallicity sequence)or the colours. Because the program considers the intrinsic scatter the age (age sequence) of the galaxies. of the data, the error estimations of the fitting parameters are We summarize now the small changes made on the KA97 reliable; otherwise the fitting errors would be greatly underes- models. The cosmological parameter q0 was changed from the timated. The regression line fits to the data are illustrated with value 0.1 used in KA97 to 0.5. Following this change, we re- the dashed lines in each of the C-M diagrams of Fig. 1. constructed the elliptical galaxy models to have an age 12 Gyr The parameter fits are summarized in Table 1, where ‘A’is instead of 15 Gyr to be consistent with the shortening of the the zero-point colour of the regression line at the absolute mag- age of the Universe. In this cosmology (q0 =0.5), the lookback nitude M0, and ‘B’ is the slope of the line in ∆(colour)/∆(mag) time of 12 Gyr corresponds to redshift z ∼ 4.5 (a lookback time as, of 15 Gyr corresponds to z ∼ 5.4 with q0 =0.1). In this pa- per, we also consider the metallicity sequence models for ages (colour) = A + B(mag − M0), down to 9 Gyr (zf =1.2). Another small difference is a change where mag and M0 are absolute magnitudes. The regression in the initial mass function slope. Hereafter, we use x =1.10 lines for the three clusters from E97 (Cl 0016+16, Cl 0054−27 instead of the value x =1.20 adopted in KA97. The reason is T and Cl 0412−65) on the V555 − I814 vs. I814 plane, defined for the following. To construct the metallicity sequence model for T. Kodama et al.: Evolution of the colour-magnitude relation of early-type galaxies in distant clusters 103

Fig. 1. C-M diagrams for the spheroidal galaxies in 6 of the clus- ters in our sample. Filled circles rep- resent the spheroidal population in each cluster. An open circle sur- rounding a filled dot represents a spectroscopically confirmed cluster member. A cross indicates an ap- parent non-member, which we have excluded from our analysis. The dashed lines show the C-M relations as defined in the text. The solid lines show the model with TG =12Gyr (zf ' 4.5). The redshifts of the models increase from bottom to top, as indicated. relatively younger ages, such as 9 − 10 Gyr, the chemical yield sented in Fig. 2. Finally, we apply an aperture correction to the is insufficient for x =1.20, since the younger age population model when necessary, as described in Sect. 3.2. needs to be made up of higher metallicity material to reproduce We have simulated the evolution of the C-M relation as a the same colours. However, the analysis is almost totally inde- function of redshift both in the observer’s frame and in the rest pendent of these small changes (KA97). The properties of the frame for various photometric systems. The response curves are metallicity sequence of elliptical galaxies are summarized in Ta- taken from Bessell (1990) for the Johnson V and the Cousins R ble 2, where MV , MG, TG, tgw, Zg(tgw), and M/LB are total and I bands, and from Bessell & Brett (1988) for the K band. absolute magnitude in V -band, total stellar mass, galactic age, The HST filter response functions for V555, R702, and I814 are time of the galactic wind, metallicity of the galactic gas at tgw, taken from the Space Telescope Science Institute web page. and mass-to-light ratio in B-band of the model galaxies at z =0, The photometric zero-points of the HST bands are taken from respectively. The luminosity-weighted mean stellar Holtzman et al. (1995). are given by two definitions; hlog Z/Z i and loghZ/Z i (see To make a precise comparison with the data, the slope of KA97). The comparison with Coma ellipticals (BLE92) are pre- the C-M relation at a given redshift is defined in the brightest 3 mag range of the model C-M relation by drawing a straight 104 T. Kodama et al.: Evolution of the colour-magnitude relation of early-type galaxies in distant clusters

Table 2. Model sequence of elliptical galaxies at z =0(TG =12 Gyr).

MV (mag) −23.00 −22.00 −21.00 −20.00 −19.00 −18.00 −17.00 9 MG(10 M ) 848 311 115 42.4 15.7 5.85 2.18 TG(Gyr) 12.00 12.00 12.00 12.00 12.00 12.00 12.00 tgw(Gyr) 0.353 0.256 0.199 0.158 0.128 0.106 0.089 metallicity hlog Z/Z i 0.061 −0.038 −0.132 −0.229 −0.328 −0.425 −0.523 sequence loghZ/Z i 0.202 0.094 −0.005 −0.101 −0.196 −0.290 −0.382 Zg(tgw) 0.566 0.417 0.298 0.188 0.084 −0.010 −0.099 M/LB 8.830 8.002 7.113 6.459 5.978 5.451 5.049 U − V 1.668 1.591 1.516 1.440 1.365 1.295 1.228 V − K 3.355 3.274 3.194 3.113 3.033 2.952 2.871

3.2. Aperture correction (a) Since early-type galaxies usually have radial colour gradients (e.g. Vader et al. 1988; Franx & Illingworth 1990; Peletier et al. 1990a; Peletier, Valentijn, & Jameson 1990b; Balcells & Peletier 1994), their colour indices will depend on the adopted aperture within which the galaxy light is integrated. Barger et al. (1996, 1997) used 5 arcsec aperture diameters to define their colour indices, which correspond to ∼ 14h−1 kpc for z =0.31 and ∼ 18h−1 kpc for z =0.5. On the other hand, BLE92 (b) used 11 arcsec apertures for their Coma cluster galaxies, which corresponds to 5h−1 kpc. Since our model for elliptical galaxies is calibrated to match the C-M relation of the Coma ellipticals in BLE92, we need to take into account the aperture differences in order to accurately compare the models with the observational data. We apply the aperture correction to the models instead of to the observational data of each cluster by constructing an aperture corrected C-M relation of Coma and recalibrating the model to match it (see KA97 for details). We adopt the value Fig. 2a and b. The C-M relation for Coma ellipticals. The filled circles ∆(V −K)/(log r/re)=−0.16 given by Peletier et al. (1990b) represent the Coma ellipticals from Bower et al. (1992). The solid lines as a typical bright elliptical galaxy colour gradient, where re is represent the loci of the metallicity sequence model with age 12 Gyr. the effective radius of the galaxy. Gonzalez´ & Gorgas (1996) recently suggested that elliptical galaxies with stronger central Mg2 indices show steeper line-strength gradients. If we con- sider the fact that the central Mg2 strength strongly correlates with the velocity dispersion of the galaxy (Bender, Burstein, T & Faber 1993; Jørgensen, Franx, & Kjærgaard 1996), then line between the two model galaxies which have MV = −23 T smaller ellipticals could have shallower colour gradients. How- and MV = −20 at z =0, respectively, which is comparable to the definition of the slope for the observational data. Note that ever, Gonzalez´ & Gorgas (1996) failed to detect significant the C-M relation for the metallicity sequence is well represented correlations of the gradients with either absolute magnitude or by a straight line within the redshift range under consideration, galaxy mass, thus we have adopted a constant colour gradient and the above definition is quite reasonable. The zero-point of for all galaxy models. We use the MK v.s. log re relation derived the model C-M relation is also defined at the absolute magnitude from the Kormendy relation of Pahre, Djorgovski, & Carvalho (1995) to apply aperture corrections to the various galaxy sizes. M0, just as was done for the observational data. Using the colour gradient and the above relation, as well as the The full tables of the evolution of the colours of ellipti- de Vaucouleurs (1948) r1/4-law for the radial profile of ellipti- cal galaxies in various combinations of age and metallicity and cals, we can reconstruct the standard C-M relation at z =0in in various photometric systems will be presented in a separate the V − K v.s. MV diagram for any given aperture using the paper in the supplement series (Kodama & Arimoto 1997, in BLE92 C-M relation for Coma. preparation). The machine readable version of the tables will also be provided upon request. The corrected C-M relations for Coma ellipticals are shown in Fig. 3 for three different physical aperture diameters, 28, 36, and 50 kpc. The first two correspond to 5 arcsec at z =0.31 T. Kodama et al.: Evolution of the colour-magnitude relation of early-type galaxies in distant clusters 105

those from SED98, 3C 324, and CIG J0848+4453, the 28 kpc aperture model is applied, even though the SED98 sample and CIG J0848+4453 actually have 20−27 kpc and 17 kpc diameter apertures, respectively. Here the apertures for SED98 clusters are provided from S.A. Stanford (private communication). This small aperture mismatch is negligible both in the slopes and in the zero-points. Note that the SED98 K magnitudes are total magnitudes and not magnitudes inside 28 kpc, hence we apply a slight correction to the 28 kpc aperture model. Since we lack aperture information on the 3C 324 data, we adopt the 28 kpc aperture model arbitrarily. The corrections in the slope and zero- point are likely to be small when compared to the observational uncertainties.

4. Comparison The model predictions for the evolution of the C-M relation are indicated by solid lines with changing redshift in Fig. 1 for the 6 clusters for which new C-M regression lines were deter- mined in this work. The model is a metallicity sequence with Fig. 3. Aperture corrected C-M relations for Coma ellipticals. Three an age of 12 Gyr (zf =4.5). As is evident from the figures, C-M relations for different apertures are constructed from the Bower et the observed C-M relations (dashed lines) are well defined in al. (1992) relation for Coma ellipticals, taking into account the aperture clusters up to z ' 1.2, and the slopes evolve almost in paral- correction (h =0.5). The Bower et al. (1992) standard C-M relation lel, in good agreement with the model. The zero-points of the is also shown. C-M relation for some of the clusters in Barger et al. (1997) deviate from the model prediction by as much as 0.2 mag. This probably arises from the zero-point uncertainties of the data. We and at z =0.5, respectively (h =0.5), while the third rep- discuss the zero-points in Sect. 4.2. The slopes of the model C- resents the relation for the whole galaxy. The C-M relation of M relations seem to globally match the observed data very well. BLE92 is indicated by the solid line. A bluing in the corrected This strongly suggests that there is no differential evolution as a C-M relation compared to that of BLE92 is observed for bright function of galaxy mass and that spheroidal galaxies in clusters galaxies (M < − 20 mag). This is because a larger aperture V ∼ form universally at high redshift. A detailed comparison with covers more of the physical size of the galaxy, which contains the models for these and the other clusters are given below. more blue light of presumably metal-poor stars. On the con- trary, fainter galaxies have smaller physical sizes, and hence a 4.1. Slopes 10 kpc aperture already covers most of the light of the galaxy and needs little correction. In spite of the bluing of the C-M The evolution of the slope of the C-M relation contains critical relations, the changes in the slope for 28 and 36 kpc apertures information on the origin of the C-M relation itself, i.e., which are tempered. This is simply because the brighter galaxies lose is the dominant factor controlling the systematic difference in more light outside the restricted aperture. The amount of dim- the photometric properties as a function of galaxy luminosity. ming compared to the total magnitudes MV in BLE92 is larger The evolution of the slope of the theoretical C-M relation is for brighter galaxies. Thus, the aperture effect on the slopes of compared with the observed data in Fig. 4. The solid lines show the C-M relation is kept rather small. For any redshift under con- the standard metallicity sequence model with TG =12Gyr sideration, the slope typically changes by only 0.01 and 0.02 per (zf ' 4.5), the same as in Fig. 1. Almost all of the clusters are mag for the 28 kpc and 36 kpc apertures compared to the 10 kpc consistent with the model prediction of this single metallicity aperture, respectively. The effect on the zero-points of the C-M sequence with old age within 1.5σ errors. As is already men- relation is negligibly small in any case (less than 0.05 mag). tioned in KA97, the metallicity sequence with an old age keeps When we compare the model to the photometric data for a the slope of the C-M relation essentially unchanged, although a given physical aperture, we regard the reconstructed C-M re- slight steepening of the slope can be seen. The dotted lines in- lation for Coma as the new standard relation, and the galaxy dicate the no-evolution models estimated by simply redshifting models are recalibrated so as to reproduce it at z =0. The the z =0models. The no-evolution models also show a slight adopted aperture for the correction of the models are 28 kpc for steepening of the slope and are very close to the prediction of AC 103, AC 114, and AC 118, and 36 kpc for Cl 0024+16, and the zf ' 4.5 metallicity sequence. This indicates that the steep- Cl 0016+16. The V555 − I814 colours for the three clusters from ening is simply due to the shift of corresponding wavelength E97 have the same 10 kpc aperture as that of BLE92, and hence shortwards with redshift. On the contrary, the dot-dashed lines no correction is applied. For the rest of the clusters, including correspond to the age sequence model; i.e., the ages become 106 T. Kodama et al.: Evolution of the colour-magnitude relation of early-type galaxies in distant clusters

Fig. 4. Evolution of the slope of the C-M relation. The solid lines represent the metallicity sequence model with zf ' 4.5 (TG =12 Gyr). The dashed lines correspond to models with different zf s, as indi- cated in the figure. The long-dashed lines show the models that change zf as a function of galaxy lumi- nosity for the brightest 3 mag range (brighter galaxies have larger val- ues of zf ). The dash-dot lines show the extreme age sequence models from KA97. The dotted lines rep- resent the no-evolution prediction (No-E). Our original results from the Barger et al. (1997) sample are shown by filled circles. The E97 and SED98 samples are indicated by filled squares and filled trian- gles, respectively. In the bottom-left panel, each observational point cor- responds respectively to following cluster in ascending redshift order: 3C 295, Cl 0412−65, GHO 1601+ 4253 (down), MS 0451.6 − 0306 (up), Cl 0016 + 16,Cl0054 − 27, 3C 220.1, and 3C 34.

younger toward fainter galaxies along the C-M relation. As is we show three metallicity sequences with younger ages: TG = evident, the pure age sequence is again absolutely rejected by 11 Gyr, TG =10Gyr and TG =9Gyr at z =0, corresponding all the clusters, which strengthens the conclusion of KA97. to zf ' 2.5, 1.7, and 1.2, respectively. In the bottom right panel Note that only AC 118 could have a somewhat steeper slope we also show the zf =1.7 model. The above models have been than the metallicity sequence model both in R702 −K and I −K recalibrated to reproduce the Coma C-M relation at the fixed age (at the 1.5σ and 2σ levels, respectively), although still far away by adjusting the mean stellar metallicity along the C-M relation. from the age sequence. The significance of the difference is However, a strong constraint on the formation epoch cannot be too small to deserve further speculation. In fact, SED98 also made due to the large uncertainties in the slope, which is defined measured the C-M slope for this cluster in a shorter wavelength for only 3 mag from the brightest end of the C-M relation. Even colour (G−K, where G denotes Gunn’s g filter) and found that it the model with zf =1.7 cannot be rejected for many clusters. does not have a significantly steeper slope than the no-evolution In Sect. 4.2 we show that the analysis of the zero-points is much Coma model. more effective in providing direct information on the average Since one of our goals is to constrain the formation epoch formation epoch of the galaxies than that of the slopes. from the C-M slope alone, we consider the younger metallicity However, the evolution of the C-M slope provides informa- sequence models as well. In the centre right panel of Fig. 4, tion on relative age variations of the early-type galaxies with T. Kodama et al.: Evolution of the colour-magnitude relation of early-type galaxies in distant clusters 107 different luminosities. Thus we can constrain the maximum al- formation epoch, as expected. Between z =0.6 and 1.0, thanks lowed age difference along the C-M relation. To do so, we in- to the small errors on the zero-points, the formation epoch of troduce now a model in which age is differentially changed as a early-type galaxies in SED98’s 5 clusters can be constrained function of galaxy luminosity. The two long-dashed lines in the to zf > 2. Beyond z =1.0,evena0.2 − 0.3 mag error is bottom right panel of Fig. 4 represent models which allow an still small enough to discriminate between a 1 Gyr difference in age difference of 1 Gyr (zf =4.5–2.5)or2Gyr(zf =4.5–1.7) galaxy age. In fact, as shown in the bottom left panel of Fig. 5, in the 3 mag range of the C-M relation with the brightest galax- the early-type galaxies in the two most distant clusters 3C 324 ies having the oldest age (zf =4.5). Note that the difference and CIG J0848 + 4453 should have a high formation epoch, is much smaller than for the age sequence, which requires a zf > 3. ∼ 7 Gyr difference. Despite the large uncertainties in the mea- For z>1 the predicted colours depend slightly on the sured slopes, the four most distant clusters can clearly reject a adopted cosmology. The bottom right panel in Fig. 5 shows −1 −1 2 Gyr age difference, since the expected slopes at high redshift alternative cosmology models with H0 =65km s Mpc would be far too steep. If our models are correct, the age dif- and q0 =0.05. Each observational zero-point has been adjusted ference is unlikely to be more than 1 Gyr, and could be much consistently with this cosmology due to a small shift of the smaller. position on the C-M line that corresponds to MK = −26 mag, Our analysis of the evolution of the C-M slope indicates where the zero-point is defined, due to the change of distance that there is little differential evolution in early-type galaxies as modulus. Note that this correction is small, 0.02 mag or less. a function of galaxy luminosity, which strongly suggests that Although the latter cosmology gives redder model colours and the bulk of the stars in early-type galaxies in rich cluster envi- the constraint on the formation epoch is slightly tempered, we ronments are coeval and form at a redshift well beyond unity. can still say that the formation epoch should be above redshift 2. Moreover, we find little difference between the C-M slopes of Even if the model uncertainties were as large as 0.2 magnitudes, different clusters, most of which are consistent with a universal the result would not be changed significantly. The bulk of the metallicity sequence with old age. This argues for a universal stars in early-type galaxies in cluster environments has to be mechanism responsible for the C-M relation of the early-type formed at z>2 even for this cosmology. galaxies in these clusters. Their photometric properties may be described primarily by only one parameter: the mean stellar 5. Discussion and conclusions metallicity controlled by their mass. We have shown that the C-M relations of early type galaxies 4.2. Zero-points in clusters with 0.31 1 even with moderately accu- 108 T. Kodama et al.: Evolution of the colour-magnitude relation of early-type galaxies in distant clusters

Fig. 5. Evolution of the zero-point of the C-M relation. The dotted line indicates the no-evolution model (No-E). The solid lines represent the metallicity sequence model with zf ' 4.5 (TG =12Gyr). The dashed lines correspond to zf ' 2.5, 1.6, and 1.2, (TG =11, 10, and 9 Gyr) from top to bottom, re- spectively. The observed data are shown by the symbols used in Fig. 4. The average and the standard de- viation of the galaxy colours in CIG J0848+44 (z =1.273) are also shown by an open circle and an er- ror bar. In the top-right panel, each observational point corresponds re- spectively to following cluster in ascending redshift order: 3C 295, Cl 0412 − 65, GHO 1601 + 4253 (up), MS 0451.6 − 0306 (down), Cl 0016 + 16,Cl0054 − 27, 3C 220.1, and 3C 34. rate photometry (errors∼ 0.1 mag). Differences of ∼ 1 Gyr are We finish with a word of caution. Our study is based on the easily measurable at such high redshifts. Therefore, photometry monolithic model for the formation of early-type galaxies. The of early-type galaxies in clusters beyond z ∼ 1 can accurately data we have analyzed here is fully consistent with this model, determine the formation epoch of these galaxies. Furthermore, but it might not be the only solution. In particular, an alternative the slope of the C-M relation at redshifts beyond z ∼ 1 is so scenario set in the context of the hierarchical merging model sensitive to age difference (as suggested by the long-dashed of galaxy formation (e.g. Kauffmann & Charlot 1997) could lines in the bottom right panel of Fig. 4) that it will allow us give results that are also broadly consistent with the available to investigate systematic difference of mean stellar age as small data, although it has not been fully confirmed yet. A detailed as '1 Gyr as a function of galactic mass, if they are present. comparison of the observed properties of the C-M relation in We expect slope changes to be especially prominent when we distant clusters with the predictions of hierarchical models that approach the star formation phase of the elliptical galaxies. properly take chemical evolution into account is clearly needed. We have not discussed the colour scatter around the C-M It is especially important to test whether this type of model can relation in this paper, but SED98 pointed out that the scatter dose give the universal C-M relation for different clusters locally and not increase with redshift out to z ∼ 1. It would be extremely over a wide range of redshift, since merging histories are likely important to determine when the C-M relation breaks down: to have varied from cluster to cluster. Moreover it is not yet i.e. when its scatter becomes very large. This would indicate the confirmed that larger ellipticals form always from larger spirals very time when the ellipticals are forming. already enriched in metal. In any case, however, if we define the formation epoch of the early-type galaxies as the time when Unfortunately, only a handfull of clusters have been found the bulk of their stars formed, the properties of the C-M relation beyond z ∼ 1. Searching for such distant clusters and pushing place that epoch well beyond z =2, independent of which the C-M relation analysis towards higher redshifts must be a formation picture is correct. promising strategy to determine the formation epoch of cluster ellipticals globally and as a function of their mass. The advent Acknowledgements. We thank R.S. Ellis, R.G. Bower and S.A. Stan- of large format near-infrared arrays provides the means to carry ford for discussions. We are grateful to S.A. Stanford for giving us out that search efficiently. continuous information of SED98 paper before publication. TK thanks T. Kodama et al.: Evolution of the colour-magnitude relation of early-type galaxies in distant clusters 109 the Japan Society for Promotion of Science (JSPS) for financially sup- porting his stay at the Institue of Astronomy, Cambridge, UK. NA thanks the JSPS for supporting his stay in Observatoire de Paris. This work was financially supported in part by a Grant-in-Aid for the Scien- tific Research (No.09640311) by the Japanese Ministry of Education, Culture, Sports and Science. AAS acknowledges generous financial support from the Royal Society.

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